Collisionless Spectral Kinetic Simulation of Ideal Multipole Resonance Probe

\textit{Active Plasma Resonance Spectroscopy} denotes a class of industry-compatible plasma diagnostic methods which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency $\omega_{\rm{pe}}$. One particular realization of \textit{APRS} with a high degree of geometric and electric symmetry is the \textit{Multipole Resonance Probe (MRP)}. The Ideal \textit{MRP(IMRP)} is an even more symmetric idealization which is suited for theoretical investigations. In this work, a spectral kinetic scheme is presented to investigate the behavior of the \textit{IMRP} in the low pressure regime. However, due to the velocity difference, electrons are treated as particles whereas ions are only considered as stationary background. In the scheme, the particle pusher integrates the equations of motion for the studied particles, the Poisson solver determines the electric field at each particle position. The proposed method overcomes the limitation of the cold plasma model and covers kinetic effects like collisionless damping.